Edit Profile (opens in new tab) Kac, Victor Co-Author Distance Author ID: kac.victor-g Published as: Kac, Victor G.; Kac, V. G.; Kac, Victor; Kac, V.; Kats, V. G.; Gatti, V. more...less Further Spellings: Kats, Viktor Gershevich; Kats, Viktor Grigor’evich; Кац Виктор Гершевич Homepage: https://math.mit.edu/~kac/index.html External Links: MGP · Wikidata · Google Scholar · Math-Net.Ru · GND · IdRef Documents Indexed: 287 Publications since 1967, including 10 Books and 16 Additional arXiv Preprints 6 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 149 Co-Authors with 233 Joint Publications 4,532 Co-Co-Authors all top 5 Co-Authors 60 single-authored 47 De Sole, Alberto 27 Wakimoto, Minoru 21 Valeri, Daniele 20 Möseneder Frajria, Pierluigi 20 Papi, Paolo 15 Bakalov, Bojko 14 van de Leur, Johan W. 12 Cantarini, Nicoletta 11 Peterson, Dale Harvey 9 Elashvili, Alexander Grigorievich 9 Liberati, Jose I. 8 De Concini, Corrado 7 Adamović, Dražen 7 Boyallian, Carina 7 Cheng, Shun-Jen 6 Gorelik, Maria 6 Jibladze, Mamuka A. 6 Perše, Ozren 5 Carpentier, Sylvain 5 D’Andrea, Alessandro 5 Heluani, Reimundo 5 Rudakov, Alexei Nikolaevich 5 Vinberg, Èrnest Borisovich 4 Procesi, Claudio 4 Radul, Andrey 4 Weisfeiler, Boris 3 Caselli, Fabrizio 3 Kazhdan, David 3 Novikov, Sergeĭ Petrovich 3 Popov, Vladimir Leonidovich 3 Raina, Ashok K. 3 Todorov, Ivan T. 3 Wang, Weiqiang 3 Zel’manov, Efim Isaakovich 2 Alekseevskiĭ, Dmitriĭ Vladimirovich 2 Arbarello, Enrico 2 Belolipetsky, Mikhail V. 2 Bokut, Leonid A. 2 Fattori, Davide 2 Frenkel, Edward V. 2 Gabber, Ofer 2 Gindikin, Simon Grigorevich 2 Jakobsen, Hans Plesner 2 Kang, Seok-Jin 2 Panyushev, Dmitri Ivanovich 2 Parshin, Alekseĭ Nikolaevich 2 Platonov, Vladimir Petrovich 2 Retakh, Alexander 2 Rozhkovskaya, Natasha 2 Shestakov, Ivan Pavlovich 2 Shvartsman, O. V. 2 Smilga, Andrei V. 2 Taĭmanov, Iskander Asanovich 2 Timashev, Dmitri A. 2 Turhan, Refik 2 Vignoli, Veronica 2 Xu, Feng 2 Yakimova, Oksana S. 2 Yan, Catherine Huafei 1 Astashov, A. M. 1 Astashova, Irina Viktorovna 1 Barakat, Aliaa 1 Beck, Jonathan 1 Bezrukavnikov, Roman 1 Bocharov, Alexei V. 1 Brylinski, Jean-Luc 1 Brylinski, Ranee Kathryn 1 Bukhshtaber, Viktor Matveevich 1 Cellini, Paola 1 Chetverikov, Vladimir N. 1 Cheung, Pokman 1 Dadok, Jiri 1 Date, Ghanashyam 1 Deodhar, Vinay V. 1 Dhar, Avinash 1 Dong, Chongying 1 Elsinger, Jason 1 Etingof, Pavel Il’ich 1 Frenkel, Igor B. 1 Fuchs, Dmitry Borisovich 1 Futorny, Vyacheslav M. 1 Gardini, Matteo 1 Godbole, Rohini M. 1 Golenishcheva-Kutuzova, Maria I. 1 Golod, Evgeniĭ Solomonovich 1 Govindarajan, Thupil R. 1 Grigorchuk, Rostislav Ivanovich 1 Guillemin, Victor W. 1 Hekmati, Pedram 1 Helemskii, Alexander Ya. 1 Hogben, Leslie 1 Iyer, Bala R. 1 Jain, Sachin 1 Kashuba, Iryna 1 Kemer, Aleksandr Robertovich 1 Kharchenko, Vladislav K. 1 Kharlampovich, Olga G. 1 Khor’kova, Nina Grigor’evna 1 Kikkawa, Keiji 1 Kolesnikov, Pavel Sergeevich ...and 65 more Co-Authors all top 5 Serials 37 Communications in Mathematical Physics 30 Advances in Mathematics 16 Journal of Mathematical Physics 13 Japanese Journal of Mathematics. 3rd Series 11 IMRN. International Mathematics Research Notices 11 Transformation Groups 7 Journal of Algebra 5 Functional Analysis and its Applications 5 Proceedings of the National Academy of Sciences of the United States of America 5 Selecta Mathematica. New Series 4 Russian Mathematical Surveys 4 Uspekhi Matematicheskikh Nauk [N. S.] 4 Inventiones Mathematicae 4 Mathematics of the USSR. Izvestiya 4 Bulletin of the American Mathematical Society. New Series 3 Communications in Algebra 3 Letters in Mathematical Physics 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Advanced Series in Mathematical Physics 3 Progress in Mathematics 2 Bulgarian Journal of Physics 2 Journal of the American Mathematical Society 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 2 Advances in Theoretical and Mathematical Physics 2 Communications in Contemporary Mathematics 2 Moscow Mathematical Journal 2 Journal of Algebra and its Applications 2 University Lecture Series 1 International Journal of Modern Physics A 1 Mathematical Notes 1 Nuclear Physics. B 1 Physics Letters. B 1 Annales de l’Institut Fourier 1 Canadian Mathematical Bulletin 1 Journal of Functional Analysis 1 Memoirs of the American Mathematical Society 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Transactions of the Moscow Mathematical Society 1 Acta Applicandae Mathematicae 1 Advances in Mathematics (Beijing) 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Indagationes Mathematicae. New Series 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Journal of Lie Theory 1 Izvestiya: Mathematics 1 Resenhas do Instituto do Matemática e Estatística da Universidade de São Paulo 1 The Asian Journal of Mathematics 1 Journal of the European Mathematical Society (JEMS) 1 International Journal of Geometric Methods in Modern Physics 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Contemporary Mathematics 1 Mathematical Sciences Research Institute Publications 1 Journal of Physics A: Mathematical and Theoretical 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 Springer Proceedings in Mathematics & Statistics 1 Transactions of A. Razmadze Mathematical Institute 1 Universitext all top 5 Fields 248 Nonassociative rings and algebras (17-XX) 61 Quantum theory (81-XX) 41 Dynamical systems and ergodic theory (37-XX) 28 Topological groups, Lie groups (22-XX) 24 Partial differential equations (35-XX) 23 Number theory (11-XX) 16 Group theory and generalizations (20-XX) 15 Algebraic geometry (14-XX) 12 Associative rings and algebras (16-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 General and overarching topics; collections (00-XX) 7 Combinatorics (05-XX) 6 Field theory and polynomials (12-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Category theory; homological algebra (18-XX) 6 Operator theory (47-XX) 5 Differential geometry (53-XX) 4 History and biography (01-XX) 4 Special functions (33-XX) 2 Functional analysis (46-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Algebraic topology (55-XX) 2 Manifolds and cell complexes (57-XX) 1 Commutative algebra (13-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 254 Publications have been cited 12,892 times in 7,481 Documents Cited by ▼ Year ▼ Infinite dimensional Lie algebras. 3rd ed. Zbl 0716.17022 Kac, Victor G. 1,492 1990 Lie superalgebras. Zbl 0366.17012 Kac, V. G. 1,181 1977 Quantum calculus. Zbl 0986.05001 Kac, Victor; Cheung, Pokman 764 2002 Vertex algebras for beginners. 2nd ed. Zbl 0924.17023 Kac, Victor 400 1998 Bombay lectures on highest weight representations of infinite dimensional Lie algebras. Zbl 0668.17012 Kac, V. G.; Raina, A. K. 287 1987 Basic representations of affine Lie algebras and dual resonance models. Zbl 0493.17010 Frenkel, I. B.; Kac, V. G. 264 1980 Infinite-dimensional Lie algebras, theta functions and modular forms. Zbl 0584.17007 Kac, Victor G.; Peterson, Dale H. 245 1984 Contravariant form for infinite-dimensional Lie algebras and superalgebras. Zbl 0574.17002 Kac, V. G. 208 1979 Infinite root systems, representations of graphs and invariant theory. Zbl 0427.17001 Kac, V. G. 189 1980 Highest weight representations of infinite-dimensional Lie algebras. Zbl 0425.17009 Kac, V. G. 182 1980 Infinite dimensional Lie algebras. An introduction. Zbl 0537.17001 Kac, Victor G. 177 1983 Vertex algebras for beginners. Zbl 0861.17017 Kac, Victor 172 1996 Infinite dimensional Lie algebras. 2nd ed. Zbl 0574.17010 Kac, Victor G. 156 1985 Some remarks on nilpotent orbits. Zbl 0431.17007 Kac, V. G. 154 1980 A sketch of Lie superalgebra theory. Zbl 0359.17009 Kac, V. G. 151 1977 Representations of quantum groups at roots of 1. Zbl 0738.17008 De Concini, Corrado; Kac, Victor G. 140 1990 Structure of representations with highest weight of infinite-dimensional Lie algebras. Zbl 0427.17011 Kac, V. G.; Kazhdan, D. A. 137 1979 Structure theory of finite conformal algebras. Zbl 0918.17019 D’Andrea, Alessandro; Kac, Victor G. 134 1998 Simple irreducible graded Lie algebras of finite growth. Zbl 0222.17007 Kac, V. G. 127 1970 Modular invariant representations of infinite-dimensional Lie algebras and superalgebras. Zbl 0652.17010 Kac, Victor G.; Wakimoto, Minoru 126 1988 Quantum reduction for affine superalgebras. Zbl 1106.17026 Kac, Victor; Roan, Shi-Shyr; Wakimoto, Minoru 126 2003 Moduli spaces of curves and representation theory. Zbl 0647.17010 Arbarello, E.; De Concini, C.; Kac, V. G.; Procesi, C. 125 1988 Infinite flag varieties and conjugacy theorems. Zbl 0512.17008 Peterson, Dale H.; Kac, Victor G. 123 1983 Spin and wedge representations of infinite-dimensional Lie algebras and groups. Zbl 0469.22016 Kac, Victor G.; Peterson, Dale H. 123 1981 Infinite-dimensional algebras, Dedekind’s \(\eta\)-function, classical Möbius function and the very strange formula. Zbl 0391.17010 Kac, V. G. 123 1978 Finite vs affine \(W\)-algebras. Zbl 1161.17015 De Sole, Alberto; Kac, Victor G. 116 2006 Quantum reduction and representation theory of superconformal algebras. Zbl 1049.17025 Kac, Victor G.; Wakimoto, Minoru 112 2004 Classification of simple Z-graded Lie superalgebras and simple Jordan superalgebras. Zbl 0367.17007 Kac, V. G. 109 1977 Modular and conformal invariance constraints in representation theory of affine algebras. Zbl 0661.17016 Kac, Victor G.; Wakimoto, Minoru 106 1988 Integrable highest weight modules over affine superalgebras and number theory. Zbl 0854.17028 Kac, Victor G.; Wakimoto, Minoru 106 1994 Cohomology of conformal algebras. Zbl 0959.17018 Bakalov, Bojko; Kac, Victor G.; Voronov, Alexander A. 105 1999 Characters of typical representations of classical Lie superalgebras. Zbl 0359.17010 Kac, V. G. 100 1977 Quasifinite highest weight modules over the Lie algebra of differential operators on the circle. Zbl 0826.17027 Kac, Victor; Radul, Andrey 99 1993 Infinite root systems, representations of graphs and invariant theory. II. Zbl 0497.17007 Kac, V. G. 96 1982 \({\mathcal W}_{1+\infty}\) and \({\mathcal W}(gl_ N)\) with central charge \(N\). Zbl 0838.17028 Frenkel, Edward; Kac, Victor; Radul, Andrey; Wang, Weiqiang 96 1995 Classification of infinite-dimensional simple linearly compact Lie superalgebras. Zbl 0929.17026 Kac, Victor G. 93 1998 Conformal modules. Zbl 1022.17018 Cheng, Shun-Jen; Kac, Victor G. 91 1997 Representations of classical Lie superalgebras. Zbl 0388.17002 Kac, V. 91 1978 Theory of finite pseudoalgebras. Zbl 1001.16021 Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G. 88 2001 Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction. Zbl 0768.17008 Frenkel, Edward; Kac, Victor; Wakimoto, Minoru 88 1992 Field algebras. Zbl 1032.17045 Bakalov, Bojko; Kac, Victor G. 88 2003 On integral representations of \(q\)-gamma and \(q\)-beta functions. Zbl 1225.33017 De Sole, Alberto; Kac, Victor G. 85 2005 Integrable highest weight modules over affine superalgebras and Appell’s function. Zbl 0980.17002 Kac, Victor G.; Wakimoto, Minoru 83 2001 Poisson vertex algebras in the theory of Hamiltonian equations. Zbl 1244.17017 Barakat, Aliaa; De Sole, Alberto; Kac, Victor G. 74 2009 Representation theory of the vertex algebra \(W_{1+\infty}\). Zbl 0862.17023 Kac, Victor; Radul, Andrey 70 1996 Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. Zbl 1294.17021 Kac, Victor G.; Raina, Ashok K.; Rozhkovskaya, Natasha 70 2013 Classification of modular invariant representations of affine algebras. Zbl 0742.17022 Kac, V. G.; Wakimoto, M. 69 1989 Realization of the basic representations of the Euclidean Lie algebras. Zbl 0476.17003 Kac, V. G.; Kazhdan, D. A.; Lepowsky, J.; Wilson, R. L. 69 1981 Vertex operator superalgebras and their representations. Zbl 0838.17035 Kac, Victor; Wang, Weiqiang 65 1994 The \(n\)-component KP hierarchy and representation theory. Zbl 1062.37071 Kac, V. G.; van de Leur, J. W. 64 2003 A new class of unitarizable highest weight representations of infinite dimensional Lie algebras. Zbl 0581.17009 Jakobsen, H. P.; Kac, V. G. 62 1985 Structure of some categories of representations of infinite-dimensional Lie algebras. Zbl 0491.17008 Deodhar, Vinay V.; Gabber, Ofer; Kac, Victor 59 1982 Quantum coadjoint action. Zbl 0747.17018 De Concini, C.; Kac, V. G.; Procesi, C. 58 1992 Classification of finite simple Lie conformal superalgebras. Zbl 1050.17023 Fattori, Davide; Kac, Victor G. 55 2002 Laplace operators of infinite-dimensional Lie algebras and theta functions. Zbl 0532.17008 Kac, Victor G. 53 1984 Automorphisms of finite order of semisimple Lie algebras. Zbl 0274.17002 Kac, V. G. 53 1969 Infinite-dimensional Lie algebras and Dedekind’s \(\eta\)-function. Zbl 0299.17005 Kac, V. G. 53 1974 Coadjoint action of a semisimple algebraic group and the center of the enveloping algebra in characteristic \(p\). Zbl 0324.17001 Kac, V.; Weisfeiler, Boris 53 1976 Polar representations. Zbl 0611.22009 Dadok, Jiri; Kac, Victor 52 1985 Classification of good gradings of simple Lie algebras. Zbl 1073.17002 Elashvili, A. G.; Kac, V. G. 51 2005 Superconformal current algebras and their unitary representations. Zbl 0599.17011 Kac, Victor G.; Todorov, Ivan T. 49 1985 Formal distribution algebras and conformal algebras. Zbl 1253.17002 Kac, Victor G. 47 1999 Quasifinite representations of classical Lie subalgebras of \({\mathcal W}_{1+\infty}\). Zbl 0938.17018 Kac, Victor G.; Wang, Weiqiang; Yan, Catherine H. 46 1998 On simplicity of vacuum modules. Zbl 1112.17023 Gorelik, Maria; Kac, Victor 43 2007 On defining relations of certain infinite-dimensional Lie algebras. Zbl 0474.17007 Gabber, Ofer; Kac, Victor G. 43 1981 Some quantum analogues of solvable Lie groups. Zbl 0878.17014 De Concini, C.; Kac, V. G.; Procesi, C. 42 1995 Classification of linearly compact simple Jordan and generalized Poisson superalgebras. Zbl 1173.17023 Cantarini, Nicoletta; Kac, Victor G. 41 2007 Irreducible representations of Lie \(p\)-algebras. Zbl 0237.17003 Weisfeiler, B. Yu.; Kac, V. G. 41 1971 Defining relations of certain infinite dimensional groups. Zbl 0625.22014 Kac, V. G.; Peterson, D. H. 40 1985 The \(n\)-component KP hierarchy and representation theory. Zbl 0843.35105 Kac, V. G.; van de Leur, J. W. 40 1993 A new \(N=6\) superconformal algebra. Zbl 0906.17020 Cheng, Shun-Jen; Kac, Victor G. 39 1997 Description of filtered Lie algebras with which graded Lie algebras of Cartan type are associated. Zbl 0317.17002 Kac, V. G. 38 1975 On automorphisms of Kac-Moody algebras and groups. Zbl 0851.17026 Kac, V. G.; Wang, S. P. 38 1992 On classification of superconformal algebras. Zbl 0938.17500 Kac, V. G.; van de Leur, J. W. 37 1989 Vacuum structure in supersymmetric Yang-Mills theories with any gauge group. Zbl 1035.81061 Kac, V. G.; Smilga, A. V. 36 2000 An elucidation of ”Infinite-dimensional algebras…and the very strange formula.” \(E^{(1)}_8\) and the cube root of the modular invariant j. Zbl 0431.17009 Kac, V. G. 36 1980 The geometry of spinors and the multicomponent BKP and DKP hierarchies. Zbl 0924.35114 Kac, Victor; van de Leur, Johan 34 1998 Exceptional hierarchies of soliton equations. Zbl 0691.17014 Kac, Victor G.; Wakimoto, Minoru 34 1989 On rationality of \(W\)-algebras. Zbl 1221.17033 Kac, Victor G.; Wakimoto, Minoru 34 2008 Affine Lie algebras and Hecke modular forms. Zbl 0457.17007 Kac, V. G.; Peterson, D. H. 34 1980 On the classification of subalgebras of \(\text{Cend}_N\) and \(\text{gc}_N\). Zbl 1034.17018 Boyallian, Carina; Kac, Victor G.; Liberati, Jose I. 33 2003 Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Zbl 1320.37031 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 33 2013 Classification of simple linearly compact \(n\)-Lie superalgebras. Zbl 1232.17008 Cantarini, Nicoletta; Kac, Victor G. 32 2010 Twisted modules over lattice vertex algebras. Zbl 1229.17028 Bakalov, Bojko; Kac, Victor G. 32 2005 Solitons in affine and permutation orbifolds. Zbl 1078.81051 Kac, Victor G.; Longo, Roberto; Xu, Feng 31 2005 Branching functions for winding subalgebras and tensor products. Zbl 0717.17017 Kac, V. G.; Wakimoto, M. 31 1990 Non-local Poisson structures and applications to the theory of integrable systems. Zbl 1286.37062 De Sole, Alberto; Kac, Victor G. 31 2013 Super boson-fermion correspondence. Zbl 0625.58041 Kac, V. G.; van de Leur, J. 30 1987 \(\Gamma\)-conformal algebras. Zbl 1031.81527 Golenishcheva-Kutuzova, Maria I.; Kac, Victor G. 30 1998 Finite linear groups whose ring of invariants is a complete intersection. Zbl 0483.14002 Kac, Victor; Watanabe, Kei-Ichi 29 1982 Sur les groupes linéaires algébriques dont l’algèbre des invariants est libre. Zbl 0343.20023 Kac, Victor G.; Popov, Vladimir L.; Vinberg, Ernest B. 29 1976 Quasi-homogeneous cones. Zbl 0163.16902 Vinberg, È. B.; Kac, V. G. 29 1967 The infinite wedge representation and the reciprocity law for algebraic curves. Zbl 0699.22028 Arbarello, E.; De Concini, C.; Kac, V. G. 28 1989 Structure of some \(\mathbb Z\)-graded Lie superalgebras of vector fields. Zbl 0988.17023 Cheng, S.-J.; Kac, V. 27 1999 Torsion in cohomology of compact Lie groups and Chow rings of reductive algebraic groups. Zbl 0566.57028 Kac, V. G. 27 1985 Some remarkable degenerations of quantum groups. Zbl 0795.17006 De Concini, C.; Kac, V. G.; Procesi, C. 27 1993 Lectures on the infinite wedge-representation and the MKP hierarchy. Zbl 0638.35070 Kac, V. G.; Peterson, D. H. 26 1986 Lie conformal algebra cohomology and the variational complex. Zbl 1225.49009 De Sole, Alberto; Kac, Victor G. 26 2009 Affine orbifolds and rational conformal field theory extensions of \(W_{1+\infty}\). Zbl 0904.17021 Kac, Victor G.; Todorov, Ivan T. 26 1997 Spinors of 13-dimensional space. Zbl 0429.20043 Gatti, V.; Viniberghi, E. 26 1978 The generalized Giambelli formula and polynomial KP and CKP tau-functions. Zbl 1517.37071 Kac, Victor; van de Leur, Johan 2 2023 Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras. Zbl 1521.37073 Kac, Victor; van de Leur, Johan 2 2023 Unitarity of minimal \(W\)-algebras and their representations. I. Zbl 07700880 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 1 2023 Polynomial tau-functions for the multicomponent KP hierarchy. Zbl 1483.14085 Kac, Victor G.; De Leur, Johan W. van 4 2022 Invariant Hermitian forms on vertex algebras. Zbl 1497.17038 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 2 2022 On Lax operators. Zbl 1522.37077 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 1 2022 Polynomial tau-functions of the KP, BKP, and the \(s\)-component KP hierarchies. Zbl 1464.37073 Kac, Victor G.; Rozhkovskaya, Natasha; van de Leur, Johan 15 2021 Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras. Zbl 1472.17084 Cantarini, Nicoletta; Caselli, Fabrizio; Kac, Victor 6 2021 Computation of cohomology of vertex algebras. Zbl 1509.17020 Bakalov, Bojko; De Sole, Alberto; Kac, Victor G. 4 2021 Classification of degenerate Verma modules for \(E(5, 10)\). Zbl 1482.17023 Cantarini, Nicoletta; Caselli, Fabrizio; Kac, Victor 4 2021 Irreducible modules over finite simple Lie pseudoalgebras. III: Primitive pseudoalgebras of type \(H\). Zbl 1511.17067 Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G. 3 2021 Classical and variational Poisson cohomology. Zbl 1487.17050 Bakalov, Bojko; De Sole, Alberto; Heluani, Reimundo; Kac, Victor G.; Vignoli, Veronica 2 2021 Yangians versus minimal \(W\)-algebras: a surprising coincidence. Zbl 1496.17011 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 2 2021 Integrability of classical affine \(W\)-algebras. Zbl 1511.17059 De Sole, Alberto; Jibladze, Mamuka; Kac, Victor G.; Valeri, Daniele 2 2021 An application of collapsing levels to the representation theory of affine vertex algebras. Zbl 1457.17020 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 9 2020 Computation of cohomology of Lie conformal and Poisson vertex algebras. Zbl 1479.17036 Bakalov, Bojko; De Sole, Alberto; Kac, Victor G. 5 2020 On the structure of quantum vertex algebras. Zbl 1431.81077 De Sole, Alberto; Gardini, Matteo; Kac, Victor G. 5 2020 \( \underline{p} \)-reduced multicomponent KP hierarchy and classical \(\mathcal{W} \)-algebras \(\mathcal{W}(\mathfrak{gl}_N,\underline{p})\). Zbl 1458.37068 Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; van de Leur, Johan 4 2020 Chiral versus classical operad. Zbl 1483.17019 Bakalov, Bojko; De Sole, Alberto; Heluani, Reimundo; Kac, Victor G. 3 2020 Poisson \(\lambda\)-brackets for differential-difference equations. Zbl 1473.37079 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; Wakimoto, Minoru 2 2020 Polynomial tau-functions of BKP and DKP hierarchies. Zbl 1421.37028 Kac, Victor; Van De Leur, Johan 17 2019 An operadic approach to vertex algebra and Poisson vertex algebra cohomology. Zbl 1471.17048 Bakalov, Bojko; De Sole, Alberto; Heluani, Reimundo; Kac, Victor G. 12 2019 Local and non-local multiplicative Poisson vertex algebras and differential-difference equations. Zbl 1421.35323 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele; Wakimoto, Minoru 7 2019 Trace functions of the parafermion vertex operator algebras. Zbl 1473.17070 Dong, Chongying; Kac, Victor; Ren, Li 3 2019 Semisimplicity sets for cyclic elements in simple Lie algebras. Zbl 1477.17060 Elashvili, A.; Jibladze, M.; Kac, V. 2 2019 Kostant pairs of Lie type and conformal embeddings. Zbl 1475.17046 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 2 2019 On Dynkin gradings in simple Lie algebras. Zbl 1436.17039 Elashvili, Alexander; Jibladze, Mamuka; Kac, Victor 1 2019 Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. I: Structural results. Zbl 1420.17028 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 25 2018 Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions. Zbl 1401.14209 Kac, Victor G.; van de Leur, Johan W. 21 2018 Classical affine \(\mathcal W\)-algebras and the associated integrable Hamiltonian hierarchies for classical Lie algebras. Zbl 1426.17015 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 18 2018 Finite \(W\)-algebras for \(\mathfrak{gl}_N\). Zbl 1398.17007 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 6 2018 A Lax type operator for quantum finite \(W\)-algebras. Zbl 1456.17008 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 5 2018 On characters of irreducible highest weight modules of negative integer level over affine Lie algebras. Zbl 1459.17042 Kac, Victor G.; Wakimoto, Minoru 3 2018 On the classification of non-equal rank affine conformal embeddings and applications. Zbl 1447.17018 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 2 2018 Lie groups, geometry, and representation theory. A tribute to the life and work of Bertram Kostant. Zbl 1412.22001 2 2018 Conformal embeddings of affine vertex algebras in minimal \(W\)-algebras. II: Decompositions. Zbl 1425.17037 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 16 2017 A remark on boundary level admissible representations. (Une remarque sur les représentations admissibles de niveau limite.) Zbl 1418.17054 Kac, Victor G.; Wakimoto, Minoru 16 2017 Introduction to vertex algebras, Poisson vertex algebras, and integrable Hamiltonian PDE. Zbl 1430.17088 Kac, Victor 6 2017 Representations of superconformal algebras and mock theta functions. Zbl 1436.17034 Kac, V. G.; Wakimoto, M. 3 2017 A characterization of modified mock theta functions. Zbl 1408.11028 Kac, Victor G.; Wakimoto, Minoru 1 2017 Structure of classical (finite and affine) \(\mathcal W\)-algebras. Zbl 1395.17063 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 21 2016 Classical affine \(\mathcal{W}\)-algebras for \(\mathfrak{gl}_N\) and associated integrable Hamiltonian hierarchies. Zbl 1433.17038 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 17 2016 Finite vs. infinite decompositions in conformal embeddings. Zbl 1405.17049 Adamović, Dražen; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Perše, Ozren 16 2016 A new scheme of integrability for (bi)Hamiltonian PDE. Zbl 1393.17048 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 13 2016 Representations of affine superalgebras and mock theta functions. II. Zbl 1372.17020 Kac, Victor G.; Wakimoto, Minoru 10 2016 Classification of linearly compact simple Nambu-Poisson algebras. Zbl 1386.17025 Cantarini, Nicoletta; Kac, Victor G. 4 2016 Representations of affine superalgebras and mock theta functions. III. Zbl 1373.17027 Kac, Victor G.; Wakimoto, Minoru 4 2016 Characters of (relatively) integrable modules over affine Lie superalgebras. Zbl 1378.17017 Gorelik, Maria; Kac, Victor G. 16 2015 Adler-Gelfand-Dickey approach to classical \(\mathcal{W}\)-algebras within the theory of Poisson vertex algebras. Zbl 1327.17024 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 16 2015 Double Poisson vertex algebras and non-commutative Hamiltonian equations. Zbl 1327.17023 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 14 2015 Conformal embeddings and simple current extensions. Zbl 1418.17059 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo; Xu, Feng 13 2015 Erratum to: “Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents”. Zbl 1327.17022 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 6 2015 On integrability of some bi-Hamiltonian two field systems of partial differential equations. Zbl 1321.37068 De Sole, Alberto; Kac, Victor G.; Turhan, Refik 5 2015 Singular degree of a rational matrix pseudodifferential operator. Zbl 1338.12006 Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G. 4 2015 Representations of affine superalgebras and mock theta functions. Zbl 1372.17019 Kac, Victor G.; Wakimoto, Minoru 15 2014 Classical \(\mathcal{W}\)-algebras and generalized Drinfeld-Sokolov hierarchies for minimal and short nilpotents. Zbl 1327.17021 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 13 2014 Dirac reduction for Poisson vertex algebras. Zbl 1368.17031 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 12 2014 Rational matrix pseudodifferential operators. Zbl 1321.35269 Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G. 8 2014 Dirac operators and the very strange formula for Lie superalgebras. Zbl 1344.17010 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 5 2014 A new approach to the Lenard-Magri scheme of integrability. Zbl 1305.37035 De Sole, Alberto; Kac, Victor G.; Turhan, Refik 4 2014 Integrability of Dirac reduced bi-Hamiltonian equations. Zbl 1326.35310 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 3 2014 Algebraic vs physical \(N = 6\) 3-algebras. Zbl 1288.81134 Cantarini, Nicoletta; Kac, Victor G. 1 2014 Bombay lectures on highest weight representations of infinite dimensional Lie algebras. 2nd ed. Zbl 1294.17021 Kac, Victor G.; Raina, Ashok K.; Rozhkovskaya, Natasha 70 2013 Classical \(\mathcal W\)-algebras and generalized Drinfeld-Sokolov bi-Hamiltonian systems within the theory of Poisson vertex algebras. Zbl 1320.37031 De Sole, Alberto; Kac, Victor G.; Valeri, Daniele 33 2013 Non-local Poisson structures and applications to the theory of integrable systems. Zbl 1286.37062 De Sole, Alberto; Kac, Victor G. 31 2013 The variational Poisson cohomology. Zbl 1290.17027 De Sole, Alberto; Kac, Victor G. 21 2013 Classification of finite irreducible modules over the Lie conformal superalgebra \(CK_{6}\). Zbl 1280.17010 Boyallian, Carina; Kac, Victor G.; Liberati, José I. 20 2013 Cyclic elements in semisimple Lie algebras. Zbl 1329.17007 Elashvili, A. G.; Kac, V. G.; Vinberg, E. B. 12 2013 Irreducible modules over finite simple Lie pseudoalgebras. II: Primitive pseudoalgebras of type \(K\). Zbl 1287.17051 Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G. 7 2013 Some remarks on non-commutative principal ideal rings. Zbl 1270.12002 Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G. 6 2013 Some algebraic properties of differential operators. Zbl 1524.12004 Carpentier, Sylvain; De Sole, Alberto; Kac, Victor G. 11 2012 Essential variational Poisson cohomology. Zbl 1297.17012 De Sole, Alberto; Kac, Victor G. 7 2012 Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs. Zbl 1335.17004 Gorelik, Maria; Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 5 2012 On complete reducibility for infinite-dimensional Lie algebras. Zbl 1225.17026 Gorelik, Maria; Kac, Victor 16 2011 Classification of linearly compact simple algebraic \(N=6\) 3-algebras. Zbl 1270.17002 Cantarini, Nicoletta; Kac, Victor G. 7 2011 Calculus structure on the Lie conformal algebra complex and the variational complex. Zbl 1317.18019 De Sole, Alberto; Hekmati, Pedram; Kac, Victor G. 3 2011 Classification of simple linearly compact \(n\)-Lie superalgebras. Zbl 1232.17008 Cantarini, Nicoletta; Kac, Victor G. 32 2010 Classification of linearly compact simple rigid superalgebras. Zbl 1269.17002 Cantarini, Nicoletta; Kac, Victor G. 16 2010 Irreducible modules over finite simple Lie conformal superalgebras of type \(K\). Zbl 1311.17005 Boyallian, Carina; Kac, Victor G.; Liberati, José I. 15 2010 On classification of Poisson vertex algebras. Zbl 1235.17020 De Sole, Alberto; Kac, Victor G.; Wakimoto, Minoru 7 2010 Denominator formulas for Lie superalgebras (extended abstract). Zbl 1373.17013 Kac, Victor; Möseneder Frajria, Pierluigi; Papi, Paolo 3 2010 Poisson vertex algebras in the theory of Hamiltonian equations. Zbl 1244.17017 Barakat, Aliaa; De Sole, Alberto; Kac, Victor G. 74 2009 Lie conformal algebra cohomology and the variational complex. Zbl 1225.49009 De Sole, Alberto; Kac, Victor G. 26 2009 On exceptional nilpotents in semisimple Lie algebras. Zbl 1252.17006 Elashvili, A. G.; Kac, V. G.; Vinberg, E. B. 9 2009 Differential conformal superalgebras and their forms. Zbl 1217.17018 Kac, Victor; Lau, Michael; Pianzola, Arturo 5 2009 On rationality of \(W\)-algebras. Zbl 1221.17033 Kac, Victor G.; Wakimoto, Minoru 34 2008 Multiplets of representations, twisted Dirac operators and Vogan’s conjecture in affine setting. Zbl 1177.17016 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 8 2008 SUSY lattice vertex algebras. Zbl 1202.81151 Heluani, Reimundo; Kac, Victor G. 4 2008 Simple Jordan conformal superalgebras. Zbl 1236.17040 Kac, Victor G.; Retakh, Alexander 3 2008 On the kernel of the affine Dirac operator. Zbl 1162.17024 Kac, Victor G.; Möseneder Frajria, Pierluigi; Papi, Paolo 1 2008 On simplicity of vacuum modules. Zbl 1112.17023 Gorelik, Maria; Kac, Victor 43 2007 Classification of linearly compact simple Jordan and generalized Poisson superalgebras. Zbl 1173.17023 Cantarini, Nicoletta; Kac, Victor G. 41 2007 Supersymmetric vertex algebras. Zbl 1205.17029 Heluani, Reimundo; Kac, Victor G. 18 2007 Characters of highest weight modules over affine Lie algebras are meromorphic functions. Zbl 1152.17011 Gorelik, Maria; Kac, Victor 2 2007 Finite vs affine \(W\)-algebras. Zbl 1161.17015 De Sole, Alberto; Kac, Victor G. 116 2006 Representations of simple finite Lie conformal superalgebras of type \(W\) and \(S\). Zbl 1111.17001 Boyallian, Carina; Kac, Victor G.; Liberati, Jose I.; Rudakov, Alexei 20 2006 Irreducible modules over finite simple Lie pseudoalgebras. I: Primitive pseudoalgebras of type \(W\) and \(S\). Zbl 1104.17006 Bakalov, Bojko; D’Andrea, Alessandro; Kac, Victor G. 17 2006 Infinite-dimensional primitive linearly compact Lie superalgebras. Zbl 1204.17017 Cantarini, Nicoletta; Kac, Victor G. 15 2006 Generalized vertex algebras. Zbl 1241.17029 Bakalov, B.; Kac, V. G. 11 2006 Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras. Zbl 1115.17009 Cantarini, Nicoletta; Kac, Victor G. 8 2006 ...and 154 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,483 Authors 146 Kac, Victor 74 Su, Yucai 53 Creutzig, Thomas 52 Li, Haisheng 47 Jing, Naihuan 46 Adamović, Dražen 42 Zhao, Kaiming 40 Tan, Shaobin 39 Dong, Chongying 39 Milas, Antun 38 De Sole, Alberto 38 Van der Jeugt, Joris 37 Zhang, Ruibin 34 Arakawa, Tomoyuki 34 Futorny, Vyacheslav M. 34 Liu, Wende 34 Misra, Kailash C. 33 Linshaw, Andrew Ross 33 Serganova, Vera V. 33 Tariboon, Jessada 33 Zhang, Yongzheng 32 Ntouyas, Sotiris K. 31 Chen, Liangyun 31 Feĭgin, Boris L’vovich 31 Jiang, Cuipo 31 Shu, Bin 31 Wang, Qing 30 Kolesnikov, Pavel Sergeevich 30 Lam, Ching Hung 30 Naito, Satoshi 30 Okado, Masato 30 Ridout, David 29 Kang, Seok-Jin 29 van de Leur, Johan W. 28 Hong, Yanyong 27 Kwon, Jae-Hoon 26 Cheng, Shun-Jen 26 Eswara Rao, Senapathi 26 Frenkel, Edward V. 26 Liu, Dong 26 Valeri, Daniele 25 Li, Chuanzhong 25 Mursaleen, Mohammad 24 Papi, Paolo 24 Yakimov, Milen T. 23 Chari, Vyjayanthi 23 Leites, Dimitry A. 23 Xu, Feng 22 Agrawal, Purshottam Narain 22 Bringmann, Kathrin 22 Elduque, Alberto 22 Gao, Yun 22 Kashiwara, Masaki 22 Kleinschmidt, Axel 22 Pei, Yufeng 22 Pianzola, Arturo 22 Stoilova, Nedjalka I. 22 Wang, Weiqiang 21 Gould, Mark D. 21 Guo, Xiangqian 21 Kaygorodov, Ivan 21 Xia, Chunguang 20 Boyallian, Carina 20 Hu, Naihong 20 Lepowsky, James 20 Sun, Jiancai 19 Gupta, Vijay 19 Lü, Rencai 19 Nicolai, Hermann 19 Palev, Tchavdar D. 19 Palmkvist, Jakob 19 Yuan, Lamei 18 Fioresi, Rita 18 Möseneder Frajria, Pierluigi 18 Oh, Se-jin 18 Sagaki, Daisuke 18 Wakimoto, Minoru 17 Bai, Chengming 17 Bakalov, Bojko 17 Budak, Hüseyin 17 Cantarini, Nicoletta 17 Gannon, Terry 17 Gorelik, Maria 17 Jimbo, Michio 17 Liberati, Jose I. 17 Nakashima, Toshiki 17 Orlov, Aleksandr Yu. 17 Poletaeva, Elena 17 Sitthiwirattham, Thanin 17 Viswanath, Sankaran 17 Yamane, Hiroyuki 16 Brundan, Jonathan 16 Fuchs, Jürgen 16 Geer, Nathan 16 Kuniba, Atsuo 16 Miwa, Tetsuji 16 Morita, Jun 16 Patureau-Mirand, Bertrand 16 Vasserot, Eric 16 Xu, Xiaoping ...and 5,383 more Authors all top 5 Cited in 484 Serials 806 Journal of Algebra 464 Communications in Mathematical Physics 413 Journal of Mathematical Physics 320 Advances in Mathematics 289 Communications in Algebra 269 Journal of High Energy Physics 236 Nuclear Physics. 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Académie des Sciences, Paris 11 Algebra and Logic 11 Demonstratio Mathematica 11 Transactions of the Moscow Mathematical Society 11 Applied Mathematics Letters 11 Turkish Journal of Mathematics 11 Boundary Value Problems ...and 384 more Serials all top 5 Cited in 60 Fields 4,574 Nonassociative rings and algebras (17-XX) 1,781 Quantum theory (81-XX) 801 Associative rings and algebras (16-XX) 750 Algebraic geometry (14-XX) 727 Group theory and generalizations (20-XX) 591 Combinatorics (05-XX) 486 Topological groups, Lie groups (22-XX) 456 Dynamical systems and ergodic theory (37-XX) 376 Number theory (11-XX) 311 Partial differential equations (35-XX) 283 Differential geometry (53-XX) 281 Special functions (33-XX) 249 Difference and functional equations (39-XX) 243 Global analysis, analysis on manifolds (58-XX) 219 Relativity and gravitational theory (83-XX) 215 Ordinary differential equations (34-XX) 198 Commutative algebra (13-XX) 198 Real functions (26-XX) 178 Category theory; homological algebra (18-XX) 178 Statistical mechanics, structure of matter (82-XX) 164 Approximations and expansions (41-XX) 161 Manifolds and cell complexes (57-XX) 144 Linear and multilinear algebra; matrix theory (15-XX) 129 Functional analysis (46-XX) 101 Several complex variables and analytic spaces (32-XX) 83 Operator theory (47-XX) 77 Functions of a complex variable (30-XX) 58 \(K\)-theory (19-XX) 58 Probability theory and stochastic processes (60-XX) 56 Algebraic topology (55-XX) 40 Numerical analysis (65-XX) 37 Geometry (51-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 33 Abstract harmonic analysis (43-XX) 33 Mechanics of particles and systems (70-XX) 32 Integral transforms, operational calculus (44-XX) 28 Computer science (68-XX) 26 Convex and discrete geometry (52-XX) 23 Order, lattices, ordered algebraic structures (06-XX) 18 Statistics (62-XX) 18 Information and communication theory, circuits (94-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Field theory and polynomials (12-XX) 13 General algebraic systems (08-XX) 13 Integral equations (45-XX) 12 Sequences, series, summability (40-XX) 10 General and overarching topics; collections (00-XX) 10 Biology and other natural sciences (92-XX) 8 Fluid mechanics (76-XX) 7 Measure and integration (28-XX) 5 History and biography (01-XX) 5 Operations research, mathematical programming (90-XX) 4 General topology (54-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Systems theory; control (93-XX) 3 Mechanics of deformable solids (74-XX) 3 Optics, electromagnetic theory (78-XX) 2 Mathematical logic and foundations (03-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Potential theory (31-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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